相关论文: Compactness results for static and dynamic chiral …
Chiral magnetic skyrmions are topological solitons, of significant physical interest, arising in ferromagnets described by a micromagnetic energy including a chiral (Dzyaloshinskii-Moriya) interaction term. We show that for small chiral…
We examine topological solitons in a minimal variational model for a chiral magnet, so-called chiral skyrmions. In the regime of large background fields, we prove linear stability of axisymmetric chiral skyrmions under arbitrary…
We consider the question of quantitative stability of minimisers for a well-known variational problem for which the infimum of the energy is not achieved in the classical sense, namely for the Dirichlet energy of degree $1$ maps from closed…
We characterize skyrmions in ultrathin ferromagnetic films as local minimizers of a reduced micromagnetic energy appropriate for quasi two-dimensional materials with perpendicular magnetic anisotropy and interfacial Dzyaloshinskii-Moriya…
Chiral symmetry breaking in magnetic thin films stabilizes new families of topological solitons that are absent in conventional anisotropic ferromagnets. Beyond the classical chiral skyrmion, which arises in uniaxial systems through the…
For 2D Hubbard model with spin-orbit Rashba coupling in external magnetic field the structure of effective spin interactions is studied in the regime of strong electron correlations and at half-filling. It is shown that in the third order…
This paper investigates the existence and qualitative properties of minimizers for a class of nonlocal micromagnetic energy functionals defined on bounded domains. The considered energy functional consists of a symmetric exchange…
The study of singular perturbations of the Dirichlet energy is at the core of the phenomenological-description paradigm in soft condensed matter. Being able to pass to the limit plays a crucial role in the understanding of the…
We investigate the properties of an effective Hamiltonian with competing interactions involving spin and chirality variables, relevant for the description of the {\it trimerized} version of the spin-1/2 {\it kagome} antiferromagnet. Using…
We report a microscopic mechanism for stabilization of biskyrmions in nature by investigating a minimal classical spin lattice model with nearest neighbour ferromagnetic Heisenberg exchange and static chiral magnetic interaction on the…
In this paper we introduce a notion of almost minimizers for certain variational problems governed by the fractional Laplacian, with the help of the Caffarelli-Silvestre extension. In particular, we study almost fractional harmonic…
We study minimizers $\boldsymbol{m}\colon \mathbb R^2\to\mathbb S^2$ of the energy functional \begin{align*} E_\sigma(\boldsymbol{m}) = \int_{\mathbb R^2} \bigg(\frac 12 |\nabla\boldsymbol{m}|^2 +\sigma^2 \boldsymbol{ m} \cdot \nabla…
We study a variational model of magnetoelasticity both in the static and in the quasistatic setting. The model features a mixed Eulerian-Lagrangian formulation, as magnetizations are defined on the deformed configuration in the actual…
Recent neutron scattering measurements on the spinel CdCr2O4 revealed a rare example of helical magnetic order in geometrically frustrated pyrochlore antiferromagnet. The spin spiral characterized by an incommensurate wavevector Q = 2pi (0,…
We study the existence and regularity of energy-minimizing harmonic almost complex structures. We have proved results similar to the theory of harmonic maps, notably the classical results of Schoen-Uhlenbeck and recent advance by…
We show that superconducting correlations in the presence of non-zero condensate velocity can mediate the peculiar interaction between localized spins that breaks the global inversion symmetry of magnetic moments. The proposed interaction…
Near-integrability is usually associated with smooth small perturbations of smooth integrable systems. Studying integrable mechanical Hamiltonian flows with impacts that respect the symmetries of the integrable structure provides an…
This paper addresses the approximation of fractional harmonic maps. Besides a unit-length constraint, one has to tackle the difficulty of nonlocality. We establish weak compactness results for critical points of the fractional Dirichlet…
The existence of compactly supported global minimisers for continuum models of particles interacting through a potential is shown under almost optimal hypotheses. The main assumption on the potential is that it is catastrophic, or not…
We consider the minimisation of power-law repulsive-attractive interaction energies which occur in many biological and physical situations. We show existence of global minimizers in the discrete setting and get bounds for their supports…